Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle rqn = 118.1^{circ}$, what is $mangle pqs$?

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle RQN$ and $\angle PQS$ are vertical angles.

Step2: Determine angle measure

Since $\angle RQN = 118.1^{\circ}$ and $\angle RQN=\angle PQS$ (vertical - angles property), then $m\angle PQS = 118.1^{\circ}$.

Answer:

$118.1$